Someone argues: "Adding a spin-orbit term to hydrogen's Hamiltonian breaks the…
PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · Atomic, Molecular & Optical Physics · One-electron atoms and the origins of atomic structure
The Structure of Quantum Mechanics, Ch Hydrogen, and the symmetry that explains it
Problem
Someone argues: "Adding a spin-orbit term λL^⋅S^ to hydrogen's Hamiltonian breaks the rotational symmetry completely, so no angular momentum quantum number survives at all. Since n=2 has eight states (four orbital states × two spin states), the spin-orbit term must split them into eight separate, non-degenerate energy levels." Find the error in this argument and give the actual level structure and degeneracies for n=2.